Leeds will reportedly pursue a new striker but do not want a return for the fan favourites.
The 31-year-old is now a free agent and reports had linked him with a return to Leeds, his former club.
And the YEP state United owner Massmio Cellino did hold meetings with Beckford's representatives - before the appointment of Uwe Rosler as the club's new head coach.
Despite being held in 'high esteem' by the Leeds faithful, however, Beckford is not on the club's shortlist.
The same, meanwhile, applies for another fan favourite and former Whites star in goalkeeper Paul Robinson, with the Elland Road outfit said to have not had any contact with the 35-year-old.
It's intriguing to see how many former Leeds stars are being released this summer, with Ian Harte, Beckford and Robinson three of them, while Luciano Becchio was released by Norwich City on Wednesday afternoon.
The need for goals is abundantly clear for the Yorkshire side, as their top scorer in the Championship last season was Mirco Antenucci on only 10 goals. It appears they don't see Beckford as an answer, however, despite reports to the contrary on Wednesday morning.